Question

The triangle in the graph is to be dilated by a scale factor of 3 with the origin as the center of dilation. If triangle A'B'C' represents the new triangle after the dilation, what are their coordinates?

A) A'(3,0) B'(6,3) C'(9,-6)
B) A(6,1) B'(9,3) C'(12,-1)
C) A(2,3) B'(3,6) C(4,-3)
D) A'(2,1) B'(3,2) C(4,-1)

Answer 1

The triangle in the graph is to be dilated by a scale factor of 3 with the origin as the center of dilation, if triangle A'B'C' represents the new triangle after the dilation, their coordinates is A) A'(3,0), B'(6,3), C'(9,-6).

Step-by-step explanation:

To dilate a triangle by a scale factor of 3 with the origin as the center, we multiply the x and y coordinates of each vertex by the scale factor.

Let's take triangle ABC, where A has coordinates (x1, y1), B has coordinates (x2, y2), and C has coordinates (x3, y3).

To find the coordinates of the dilated triangle A'B'C', we multiply each coordinate by 3:
A' = (3 * x1, 3 * y1)
B' = (3 * x2, 3 * y2)
C' = (3 * x3, 3 * y3)

In this case, the correct answer is A) A'(3,0), B'(6,3), C'(9,-6).